1. Field of the Invention
The present invention generally relates to a method, system and software product used in three-dimensional non-linear finite element analysis of a structure, more particularly to simulating fracture propagation in brittle materials.
2. Description of the Related Art
Finite element analysis (FEA) is a computerized method widely used in industry to model and solve engineering problems relating to complex systems such as three-dimensional non-linear structural design and analysis. FEA derives its name from the manner in which the geometry of the object under consideration is specified. With the advent of the modern digital computer, FEA has been implemented as FEA software. Basically, the FEA software is provided with a model of the geometric description and the associated material properties at certain points within the model. In this model, the geometry of the system under analysis is represented by solids, shells and beams of various sizes, which are called elements. The vertices of the elements are referred to as nodes. The model is comprised of a finite number of elements, which are assigned a material name to associate with material properties. The model thus represents the physical space occupied by the object under analysis along with its immediate surroundings. The FEA software then refers to a table in which the properties (e.g., stress-strain constitutive equation, Young's modulus, Poisson's ratio, thermo-conductivity) of each material type are tabulated. Additionally, the conditions at the boundary of the object (i.e., loadings, physical constraints, etc.) are specified. In this fashion a model of the object and its environment are created.
FEA is becoming increasingly popular with automobile manufacturers for optimizing both the aerodynamic performance and structural integrity of vehicles. Similarly, aircraft manufacturers rely on FEA to predict airplane performance long before the first prototype is built. Rational design of semiconductor electronic devices is possible with Finite Element Analysis of the electrodynamics, diffusion, and thermodynamics involved in this situation. FEA is utilized to characterize ocean currents and distribution of contaminants. FEA is being applied increasingly to analysis of the production and performance of such consumer goods as ovens, blenders, lighting facilities and many plastic products. In fact, FEA has been employed in as many diverse fields as can be brought to mind, including plastics mold design, modeling of nuclear reactors, analysis of the spot welding process, microwave antenna design, simulating of car crash and biomedical applications such as the design of prosthetic limbs. In short, FEA is utilized to expedite design, maximize productivity and efficiency, and optimize product performance in virtually every stratum of light and heavy industry. This often occurs long before the first prototype is ever developed.
On the most challenging FEA tasks is to simulate fracture (e.g., crack, micro-crack) propagation in brittle materials such as glasses, ceramics, and hard composites. Fracture usually begins when stress applied to a material is concentrated at the tip of a micro-crack. When the stress exceeds a critical value, atomic bonds begin to break, elastic energy is released, and new surface is created as the crack propagates in the material. Brittle fracture is not only an annoying everyday experience or a safety hazard, but also an important technological process for the shaping of hard materials. Controlling the brittle fracture of flint-stone was the crucial step into the stone-age and polishing silicon wafers of 300 mm diameter with tolerable height variations of only a few atom spacing is a technological challenge today. Engineers at the beginning of the last century started to investigate brittle fracture processes and soon realized that the mechanical stress in the solid is concentrated at the crack tip. This stress concentration increases with increasing sharpness of the crack. In a brittle material, the crack tip is atomically sharp and, therefore, the material must sustain very high stresses exceeding the nominal fracture strength of engineering materials.
Fracture can be categorized into three fundamental modes: FIG. 1A shows an opening or normal mode which is designated as Mode-I 100A; FIG. 1B shows a forward shear or sliding mode designated as Mode-II 100B; and FIG. 1C shows a transverse shear or tearing mode designated as Mode-III 100C. These three fracture modes can occur separately or in any combination. Fractures in which two or more modes were operative are termed mixed-mode fractures. Today, all of the existing fracture propagation simulation schemes have problems. Some schemes require same fracture energy release rate for all three modes, some assume a simplified linear, bilinear or trilinear traction-separation law, some do not differentiate Mode-II and Mode-III, while others do not enforce the irreversible condition.
Therefore, there is a need to have a set of general cohesive laws that include all three fracture modes interacting with each other for simulating fracture in brittle material.